Z-Score Calculator
Z-Score Calculator
Enter a value, the dataset's mean, and its standard deviation. This calculates the z-score — a standardized measure of how many standard deviations that value is above or below the mean.
A positive z-score means the value sits above the mean, a negative z-score means below it, and the magnitude tells you exactly how many standard deviations away it is — a z-score of 2 is unusually far from the mean in a roughly bell-curve-shaped dataset, while a z-score near 0 is close to typical. Standardizing values into z-scores is what makes it possible to fairly compare numbers drawn from entirely different distributions — a test score, a height measurement, and a stock return can all be placed on the same standardized scale for comparison.
- Formula: Z = (Value − Mean) ÷ Standard Deviation.
- Reading a z-score: a positive z-score means the value is above the mean, negative means below, and 0 means exactly at the mean — the magnitude tells you how many standard deviations away it is.
- Why standardize? z-scores let you compare values from different distributions (like test scores on different scales) on a common, unit-free scale.
What counts as an "unusual" z-score?
In a roughly normal distribution, about 95% of values fall within z-scores of −2 to +2, and about 99.7% fall within −3 to +3 — values beyond ±2 or ±3 are often flagged as unusual or outliers.
Can I use this with any dataset, or only normal distributions?
The z-score formula itself works for any dataset, but the standard interpretation guidelines (like the 95%/99.7% rule) specifically assume a roughly normal (bell-curve) distribution.
Z-Score Calculator
Enter a value, the dataset's mean, and its standard deviation. This calculates the z-score — a standardized measure of how many standard deviations that value is above or below the mean.
A positive z-score means the value sits above the mean, a negative z-score means below it, and the magnitude tells you exactly how many standard deviations away it is — a z-score of 2 is unusually far from the mean in a roughly bell-curve-shaped dataset, while a z-score near 0 is close to typical. Standardizing values into z-scores is what makes it possible to fairly compare numbers drawn from entirely different distributions — a test score, a height measurement, and a stock return can all be placed on the same standardized scale for comparison.
- Formula: Z = (Value − Mean) ÷ Standard Deviation.
- Reading a z-score: a positive z-score means the value is above the mean, negative means below, and 0 means exactly at the mean — the magnitude tells you how many standard deviations away it is.
- Why standardize? z-scores let you compare values from different distributions (like test scores on different scales) on a common, unit-free scale.
What counts as an "unusual" z-score?
In a roughly normal distribution, about 95% of values fall within z-scores of −2 to +2, and about 99.7% fall within −3 to +3 — values beyond ±2 or ±3 are often flagged as unusual or outliers.
Can I use this with any dataset, or only normal distributions?
The z-score formula itself works for any dataset, but the standard interpretation guidelines (like the 95%/99.7% rule) specifically assume a roughly normal (bell-curve) distribution.